The Bulls entered administration back in January, resulting in a six-point deduction at the start of the season.
Green, who is the managing director of Safeguard Security Group, fought off rival bids from Richard Lamb's London-based consortium and Mandy Koukash, wife of Salford Red Devils chairman Marwan Koukash.
"I am really pleased to have completed the takeover of this fantastic club," he told Bradford's official website.
"Bradford Bulls is a major sporting brand in the United Kingdom and I think this has been proven by the sheer volume of national media coverage which the club has received throughout the process of its future being secured.
"Now that the takeover is complete, the team and I are in a position to move forward with the business."